When Key Fragments Should Drop?

I suppose I should not be too critical of a system designed to give players "free" skins and such, but it just feels really uncomfortable to be slowly collecting chests all the time with no real way to open all of them. Getting a single key fragment is so much harder than getting a chest, and you need THREE of them to get a chest. I play for a good two hours or so every day, and am lucky if I can get even two or three keys in a month, let alone enough to open all my chests. I don't want to spend all of my time playing LoL, but it seems like the only option out there is just to play an obscene amount in order to get enough keys.

Of course, I would not post about a problem without a solution. My idea is this, that the more chests you have than keys, the higher the chance of obtaining a key fragment when you win a game. That way everyone sitting on 7 chests who only plays a casual amount will still be rewarded for obtaining the chests, instead of only being concerned about key fragments and just hoping they get lucky.

Plus my ocd about the ever growing amount of chests in my account can be put to rest knowing that my pile will not keep growing indefinitely.

Thoughts?